Space of modular forms of level 197, weight 2, and Character 197.d

• Label: 197.2.d
• Level: $197$
• Weight: $2$
• Character orbit: 197.d
• Rep. character: $\chi_{197}(36,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $90$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(197, [\chi])\).

	Total	New	Old
Modular forms	102	102	0
Cusp forms	90	90	0
Eisenstein series	12	12	0

Trace form

90 * q - 2 * q^2 - 5 * q^3 - 26 * q^4 + q^5 - 10 * q^6 - 11 * q^7 - 16 * q^9 + 9 * q^10 - 7 * q^11 + 15 * q^12 + 9 * q^13 - 40 * q^14 - 16 * q^15 - 10 * q^16 + 13 * q^17 + 15 * q^18 - 20 * q^19 + 26 * q^20 + 13 * q^21 - 17 * q^22 + 25 * q^23 - 17 * q^24 + 16 * q^25 - 2 * q^26 - 41 * q^27 - 50 * q^28 - 33 * q^29 - 72 * q^30 - 15 * q^31 + 46 * q^32 - 32 * q^33 + 31 * q^34 + 45 * q^35 - 64 * q^36 - 27 * q^37 + 43 * q^38 + 14 * q^39 + 31 * q^40 + 35 * q^41 + 14 * q^42 + 16 * q^43 + 49 * q^44 - 8 * q^45 + 17 * q^46 - 4 * q^47 + 41 * q^48 - 48 * q^49 - 52 * q^50 + 51 * q^51 - 2 * q^52 + 41 * q^53 + 14 * q^54 + 53 * q^55 + 52 * q^56 - 104 * q^57 - 79 * q^58 - 17 * q^59 + 11 * q^60 + 21 * q^61 + 23 * q^62 + 48 * q^63 + 22 * q^64 + 5 * q^65 - 94 * q^66 - 5 * q^67 - 200 * q^68 + 54 * q^69 + 64 * q^70 - 94 * q^71 + 75 * q^72 + 31 * q^73 + 18 * q^74 + 36 * q^75 - 80 * q^76 + 22 * q^77 - 45 * q^78 - 25 * q^79 + 131 * q^80 + 6 * q^81 + 51 * q^82 - 130 * q^83 + 108 * q^84 - 129 * q^85 + 32 * q^86 + 98 * q^87 + 54 * q^88 + 17 * q^89 - 42 * q^90 - 119 * q^91 + 31 * q^92 + 60 * q^93 - 111 * q^94 - 77 * q^95 - 98 * q^96 + 49 * q^97 + 45 * q^98 + 25 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
197.2.d.a	$197$	$2$	197.d	197.d	$7$	$90$	$15$	$1.573$		None		✓	✓	✓	197.2.d.a	$2$	$0$	\(-2\)	\(-5\)	\(1\)	\(-11\)		$\mathrm{SU}(2)[C_{7}]$